# Specific heat capacity

The specific heat capacity of a substance is defined as the quantity of heat required to raise the temperature of a unit mass of substance, through the a degree rise in temperature.( 1oC of 1k) . The quantity of heat received by the substance is directly proportional to the mass, change in temperature and the nature of material. That is

$Q\quad \propto \quad m(\theta 2\quad -\theta 1)\quad or\quad Q\quad =\quad cm(\theta 2-\theta 1)\quad where\quad c=specific\quad hetat\quad capacity$

Q = quantity of heat, and m = unit mass, from the equation above specific heat capacity can be given as

$c\quad =\quad \frac { Q }{ m(\theta 2-\theta 1) }$

The of Jkg-1k-1,

Substance and their specific heat capacity in Jkg-1K-1

Lead =130    Mercury = 140   Brass = 380   Zinc = 380 Copper = 400Iron = 450, Glass = 670 ,

Aluminum = 900,  Ice = 2100, methylated spirit= 2400, Sea water =3900, Water =4200

# Heat capacity

It is being defined as the quantity of heat required to raise the temperature through one degree rise in temperature. It is give as

h = cm, where h = heat capacity, c = specifics heat capacity and m = the entire mass of the body. The unit is also in JKg-1K-1

Example1. Calculate the mass of iron with heat capacity of 900JKg-1K-1,

Solution, using h = cm

M = h/c but h = 900JKg-1K-1, c = 450JKg-1K-1     then,

$c=\frac { 900 }{ 450 } =2.0kg$

Example2, What quantity of heat is needed to raise the temperature of 20kg of aluminium through 10k

#### Solution,  using   Q = cm (Ѳ2-Ѳ1)

But c = 900JKg-1K-1, m = 20kg and  (Ѳ2-Ѳ1) = 10K therefore,

$Q\quad =\quad 900\times 20\times 10=180,000\quad =\quad 18\times { 10 }^{ 4 } J$

Example 3, What is the  heat capacity of 20kg of brass.

Solution, Using  h = cm, where h = heat capacity, c = specific heat capacity of brass = 380JKg-1K-1, and = 20kg

$therefore\quad h\quad =380\quad \times \quad 30\quad =7600K{ J }^{ -1 }$

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